Since the original data are mixed-frequency time series. To solve this problem, the frequency of all indices used in this study was chosen as quarterly. Besides, to solve the inconsistency of time length, i.e. different starting time of all indices, I used the subset series of the longest common length which starts in 1960 Q1 and ends in 2020 Q1.
All index series are standardized before we do any statistical analysis, that is, centering each series (makes its mean equal to 0) and multiplying a constant to each series to make its variances equal to 1. For example, the value scale of Private Housing Units Permits Total SAAR (thousands) is much greater than else. By standardized the data series, we may ignore how magnificent of its value but the relationship between it and other series. Taking advantages of those internal relationship, we can group economic time periods into different regimes and learn how to make strategies for different economic regimes.
Through looking into the correlation between each pairs of standardized indices, we can detect that some of indices are closely correlated with each other. Since we already have 13 indices Therefore, we can use some dimension reduction techniques in statistics like PCA.
## The correlation between US Real GDP (QoQ, %, SAAR) and
## US Manufacturing New Orders Total MoM SA is 0.44 .
## The correlation between US Real GDP (QoQ, %, SAAR) and
## US Nominal Account Balance (Billions USD) is 0.516 .
## The correlation between US CPI (inflation) Urban Consumer YoY NSA and
## US Unemployment Rate (%) is 0.719 .
## The correlation between US CPI (inflation) Urban Consumer YoY NSA and
## US Industrial Production MoM SA is 0.709 .
## The correlation between US CPI (inflation) Urban Consumer MoM SA and
## US Employment on Nonfarm Payrolls Total (SA, Net Monthly Change, thousands) is 0.662 .
## The correlation between US Unemployment Rate (%) and
## US Industrial Production MoM SA is 0.516 .
## The correlation between US Industrial Production MoM SA and
## Conference Board US Leading Economic Indicator is 0.495 .
## The correlation between US Manufacturing New Orders Total MoM SA and
## US Nominal Account Balance (Billions USD) is 0.681 .
## The correlation between US Manufacturing New Orders Total MoM SA and
## Federal Reserve Money Supply M2 YoY % Change is 0.501 .
## The correlation between US Nominal Account Balance (Billions USD) and
## Federal Reserve Money Supply M2 YoY % Change is 0.428 .
The plot below shows the contributions of variables in accounting for the variability to the top 2 principal components, that is, the higher contribution (%) of one economic index in this graph, the greater necessity to including this index into our analysis.
Some highly correlated indices result trivial variables which do not contribute variance to first two principle components.
Individuals with a similar profile are grouped together.
Positive correlated variables point to the same side of the plot. Negative correlated variables point to opposite sides of the graph.
How about removing those redundant variables?
2020 is extremely unusual, far away from any previous annual index performance. How about removing the data of 2020?
Now, our data become more dispersive.
K-means clustering (MacQueen 1967) is one of the most commonly used unsupervised machine learning algorithm for partitioning a given data set into a set of k groups (i.e. k clusters), where k represents the number of groups pre-specified by the analyst. It classifies objects in multiple groups (i.e., clusters), such that objects within the same cluster are as similar as possible (i.e., high intra-class similarity), whereas objects from different clusters are as dissimilar as possible (i.e., low inter-class similarity).
Now, we repeated the analysis using quarterly data
